Spacecraft that operate in middle Earth orbits (MEO) or lower orbits typically use magnetic torquers for Reaction Wheel Assembly (RWA) momentum control. By applying current to one or more torquer coils, a magnetic dipole is generated that interacts with the Earth's magnetic field to produce an external torque on the spacecraft. Spacecraft in MEO or lower orbits (LEO) use magnetic torquing because it is more mass efficient than thruster torquing, which must use propellant stored on board the spacecraft. In addition, magnetic torquing also provides the advantage of not perturbing the spacecraft orbit, which occurs with thruster torquing, because no forces are applied to the spacecraft during magnetic torquing. This is important for missions such as GPS, where it is desirable not to perturb the spacecraft orbit because precise orbital knowledge accuracy must be maintained at all times.
Prior-art magnetic momentum control (MMC) systems operate on the total spacecraft momentum error or the RWA momentum error that exists at any given time. At each control cycle, the torquer current or “on time” is commanded so as to reduce the present momentum error. One drawback of this approach is that torques are applied to reduce the effects of both cyclic (periodic) and secular momentum components. This approach wastes control authority and power by applying torque to reduce cyclic components that don't result in momentum growth. Another problem is that some portions of the orbit may have more favorable magnetic control geometry than others, yet the prior-art algorithm does not take into account how the magnetic field varies over the orbit. These deficiencies impact the magnetic torquer sizing, resulting in the need for larger torquers and more torquer power than necessary to control the RWA momentum.
Specifically, conventional MMC systems calculate the control torque that needs to be applied by each torquer based on the instantaneous system momentum error. In general, the control torque generated by each magnetic torquer, denoted by the subscript i, is computed using Equation 1 as the cross product between the torquer dipole moment vector and the instantaneous local magnetic field vector.Ti(t)=mi(t)×B(t)  (1)
The magnetic field vector mi(t) depends on the spacecraft orbit position. It may be estimated using an Earth magnetic field model or may be measured using a magnetometer. Such vectors are typically expressed in an inertial coordinate frame and, therefore, the torquer dipole moment vector, which is fixed in the body frame, also varies as a function of the spacecraft attitude.
Such a conventional MMC system generally operates with a sampling period of ts (the time interval between samples) and attempts to drive the total system momentum to zero (the sum of the spacecraft body momentum and the RWA momentum). For this conventional system, the torquer duty cycles (the ratio of the torquer commanded on-times to the sampling period) may be computed using Equation 2. The computed duty cycle may be a positive value or a negative value. In the case that the duty cycle value is negative, the current to the torquer is reversed (reverse polarity).
      [                                                      dc              1                        ⁡                          [              k              ]                                                                                      dc              2                        ⁡                          [              k              ]                                            ]    =                    -                  1                      t            s                              ⁢      K        +                  H        sys            ⁡              [        k        ]            whereK+=pseudoinverse([T1[k]T2[k]])  (2)andHsys[k]=Hs/c[k]+Hrwa[k]
Computing the control torques by using the pseudo-inverse of the control torque matrix, as shown above, minimizes the torquer duty cycles given the orientation of the torquer torque vectors and the Earth's magnetic field. This approach also reduces the overall RWA speeds. However, as mentioned above, a major disadvantage of this conventional MMC control method is that it responds to the total momentum error, including the momentum changes that are periodic over one orbit. These periodic (or cyclic) momentum changes may be large at times, but do not increase RWA speeds over an orbit. Therefore, responding to the cyclic momentum components wastes power and torquer control authority. Furthermore, in using the conventional approach, the applied torque depends on only the present Earth magnetic field vector. The conventional MMC method therefore wastes power by torquing to the maximum extent possible at all orbit positions, regardless of whether or not favorable geometry exists based on changes in the Earth magnetic field vector as the spacecraft changes position during the orbit.
In a spacecraft that uses reaction wheel assemblies (RWAs) for momentum control, the applied RWA torque must counteract the effects of environmental disturbance torques acting on the spacecraft body, thereby causing the magnitude of the RWA speeds to increase over time. The environmental disturbances, which include torques due to solar radiation pressure, gravity gradient and radio frequency (RF) transmissions, may be large for a spacecraft with large deployed antennas and solar arrays, such as a next-generation GPS spacecraft.
For spacecraft that experience large disturbance torques, using conventional MMC systems that apply magnetic torques to null a momentum error that includes both secular and periodic components requires the use of increased duty cycles and power to the magnetic torquers and/or larger torquers, which are heavy, require increased power, and are difficult to accommodate on the spacecraft panels.
In view of the above, a need exists for a more efficient magnetic momentum control system that responds to the secular momentum error component while ignoring the cyclic momentum components, that takes into account the variations of the Earth's magnetic field over the entire orbit of the spacecraft, and that applies magnetic momentum control torques where it is most efficient to do so.